In general, when manufacturing the silicon single crystal, a diameter of the single crystal is controlled by using the pull-up speed of the single crystal and a heater temperature as manipulated variables. For example, there is disclosed a method for manufacturing a silicon single crystal of growing the silicon single crystal by independently controlling an average pull-up speed and the heater temperature by using the Czochralski method (see, for example, Japanese Patent Application Laid-Open No. 2005-082474 (paragraphs [0011], [0012] and [0014])). In this method for manufacturing the silicon single crystal, a silicon single crystal growing length which is obtained per unit time of intervals of 30 min to 50 min while the silicon single crystal is being grown is defined as the average pull-up speed, and in a steady state, the average pull-up speed is fixed to a constant speed and in an unsteady state, the pull-up speed is fluctuated for a predetermined time in accordance with a deviation between an estimated crystal diameter and a target crystal diameter of the diameter of the crystal which is being grown, and in the steady state, the heater temperature is maintained constant and in the unsteady state, the heater temperature is fluctuated in accordance with the deviation between the estimated crystal diameter and the target crystal diameter of the diameter of the crystal which is being grown, and thereby the diameter of the single crystal is controlled. Here, the predetermined time for which the pull-up speed is fluctuated is a time which is shortened to such an extent (a fluctuation range is within ±0.02 mm/min) that no great influence is exerted onto the average pull-up speed which is fixed in the steady state and it is preferable that this time be not more than 30 seconds. By the method for manufacturing the silicon single crystal so configured, efficient pulling-up of the silicon single crystal which is reduced in crystal defects is attained
On the other hand, there is disclosed a method for manufacturing a single crystal of controlling the pull-up speed moving average value which has a causal relationship with the quality of the single crystal (see, for example, Japanese Patent Application Laid-Open No. 2010-053015 (paragraphs [0007] to [0009], [0011] to [0013])). In this method for manufacturing the single crystal, the diameter of the single crystal is controlled by repetitively performing the step of calculating a set value of the single crystal pull-up speed, the step of calculating upper and lower limit values of the manipulated variable of the single crystal pull-up speed and the step of controlling the pull-up speed moving average value on the basis of the above-mentioned set value and the upper and lower limit values of the above-mentioned manipulated variable in a process of pulling up the single crystal by the Czochralski method. In addition, the upper and lower limit values of the manipulated variable of the pull-up speed are calculated such that the pull-up speed moving average value falls within a permissible range which has been set in advance, the diameter is controlled in that constraint condition and thereby also the pull-up speed moving average value is controlled so as to be within the permissible range which has been set in advance. Further, before starting pulling-up of the single crystal, the target value of the pull-up speed is set in advance for every pull-up length and the pull-up speed of the single crystal is corrected such that an actual measured value of the pull-up speed moving average value matches the target value.
In the method for manufacturing the single crystal so configured, the diameter of the single crystal is controlled by repetitively performing the step of calculating the set value of the single crystal pull-up speed and the upper and lower limit values of the manipulated variable of the pull-up speed and the step of controlling the pull-up speed moving average value of the single crystal on the basis of the above-mentioned set value and the above-mentioned upper and lower limit values of the manipulated variable of the pull-up speed. That is, since the pull-up speed moving average value of the single crystal is controlled every moment, quality dispersion in an axial direction of the single crystal is reduced. Consequently, the single crystal of high quality is stably manufactured. In addition, since the upper and lower limit values are calculated such that the pull-up speed moving average value falls within the permissible range, the quality dispersion in the axial direction of the single crystal is more reduced and the single crystal of high quality is manufactured more stably. Further, since the target value of the pull-up speed is set in advance before starting pulling-up of the single crystal and the pull-up speed of the single crystal is corrected such that the actual measured value of the moving average value of the pull-up speed matches the target value thereof, the pull-up speed of the single crystal is optimized, the quality diversion in the axial direction of the single crystal is more reduced and the single crystal of high quality is more stably manufactured.